%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA007+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:23:34 PM UTC 2026
% Result : Theorem 10.95s 4.06s
% Output : CNFRefutation 10.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 184 ( 26 unt; 0 def)
% Number of atoms : 750 ( 252 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 948 ( 382 ~; 424 |; 119 &)
% ( 3 <=>; 15 =>; 0 <=; 5 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 5 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 433 ( 0 sgn 403 !; 30 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(f3,axiom,
( complete
=> ! [X0,X1] :
( ( X0 != X1
& vertex(X1)
& vertex(X0) )
=> ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( in_path(X3,X2)
& path(X0,X1,X2) )
=> ( ? [X4] :
( ( X3 = tail_of(X4)
| X3 = head_of(X4) )
& on_path(X4,X2) )
& vertex(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',in_path_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0] :
( ~ edge(X0)
| ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f24,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f25,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(flattening,[],[f24]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ in_path(X3,X2)
| ~ path(X0,X1,X2)
| ( ? [X4] :
( ( X3 = tail_of(X4)
| X3 = head_of(X4) )
& on_path(X4,X2) )
& vertex(X3) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in_path(X3,X2)
| ~ path(X0,X1,X2)
| ( ? [X4] :
( ( X3 = tail_of(X4)
| X3 = head_of(X4) )
& on_path(X4,X2) )
& vertex(X3) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f36,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(flattening,[],[f37]) ).
fof(f47,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f48,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) ) ) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f50,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ( ( ( tail_of(sK0(X0,X1)) = X1
& head_of(sK0(X0,X1)) = X0 )
| ( tail_of(sK0(X0,X1)) = X0
& head_of(sK0(X0,X1)) = X1 ) )
& ( tail_of(sK0(X0,X1)) != X1
| head_of(sK0(X0,X1)) != X0
| tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X1 )
& edge(sK0(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f50]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ in_path(X3,X2)
| ~ path(X0,X1,X2)
| ( ( tail_of(sK3(X2,X3)) = X3
| head_of(sK3(X2,X3)) = X3 )
& on_path(sK3(X2,X3),X2)
& vertex(X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X2,X3))],[f32]) ).
fof(f57,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(X0,X3,X4)) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X6,sK4(X0,X3,X4))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ( path(X0,X1,sK5(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f65]) ).
fof(f68,plain,
( complete
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12)
& ! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f48]) ).
fof(f70,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f72,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X1
| head_of(sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f75,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f77,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| in_path(head_of(X3),X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ in_path(X3,X2)
| ~ path(X0,X1,X2)
| vertex(X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f38]) ).
fof(f123,plain,
complete,
inference(cnf_transformation,[],[f68]) ).
fof(f124,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f68]) ).
fof(f125,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f68]) ).
fof(f126,plain,
! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_51,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in_path(head_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in_path(tail_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( vertex(X3)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X3,X4,X2)
| ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_92,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X0,X3)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_93,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,X0,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_103,negated_conjecture,
! [X0: $i] :
( ~ edge(X0)
| ( tail_of(X0) != head_of(sK11) )
| ( head_of(X0) != tail_of(sK10) ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_104,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f125]) ).
tcf(c_105,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f124]) ).
tcf(c_106,negated_conjecture,
complete,
inference(cnf_transformation,[],[f123]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_106,c_52]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_144]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_106,c_57]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_157]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_106,c_56]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_160]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_106,c_55]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_162]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_54,c_106,c_54]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_164]) ).
tcf(c_227,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_165]) ).
tcf(c_228,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_163]) ).
tcf(c_229,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_161]) ).
tcf(c_230,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_158]) ).
tcf(c_235,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( edge(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2))
| ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_145]) ).
tcf(c_236,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(subtyping,[status(esa)],[c_105]) ).
tcf(c_237,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(subtyping,[status(esa)],[c_104]) ).
tcf(c_238,negated_conjecture,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ~ edge(X0_iProver_sequential_2)
| ( tail_of(X0_iProver_sequential_2) != head_of(sK11) )
| ( head_of(X0_iProver_sequential_2) != tail_of(sK10) ) ),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_246,negated_conjecture,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2)
| ~ precedes(X1_iProver_sequential_2,X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_93]) ).
tcf(c_247,negated_conjecture,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_2: iProver_sequential_2,X2_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2)
| ~ precedes(X2_iProver_sequential_2,X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ( tail_of(X1_iProver_sequential_2) != tail_of(X2_iProver_sequential_2) )
| ( head_of(X0_iProver_sequential_2) != head_of(X1_iProver_sequential_2) ) ),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_250,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2)
| ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_256,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_2: iProver_sequential_2] :
( on_path(X1_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_257,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_2: iProver_sequential_2] :
( on_path(X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_258,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_2: iProver_sequential_2] :
( precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ sequential(X0_iProver_sequential_2,X1_iProver_sequential_2)
| ~ on_path(X1_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ on_path(X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_263,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2] :
( sequential(X0_iProver_sequential_2,X1_iProver_sequential_2)
| ( X0_iProver_sequential_2 = X1_iProver_sequential_2 )
| ~ edge(X1_iProver_sequential_2)
| ~ edge(X0_iProver_sequential_2)
| ( head_of(X0_iProver_sequential_2) != tail_of(X1_iProver_sequential_2) ) ),
inference(subtyping,[status(esa)],[c_75]) ).
tcf(c_266,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X2_iProver_shortest_path_2: iProver_shortest_path_2] :
( vertex(X2_iProver_shortest_path_2)
| ~ in_path(X2_iProver_shortest_path_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_72]) ).
tcf(c_267,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( in_path(tail_of(X0_iProver_sequential_2),X0_iProver_number_of_in_2)
| ~ on_path(X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_268,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( in_path(head_of(X0_iProver_sequential_2),X0_iProver_number_of_in_2)
| ~ on_path(X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_269,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2,X0_iProver_number_of_in_2: iProver_number_of_in_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( edge(X0_iProver_sequential_2)
| ~ on_path(X0_iProver_sequential_2,X0_iProver_number_of_in_2)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_number_of_in_2) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_279,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( vertex(tail_of(X0_iProver_sequential_2))
| ~ edge(X0_iProver_sequential_2) ),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_283,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] : X0_iProver_shortest_path_2 = X0_iProver_shortest_path_2,
theory(equality) ).
tcf(c_284,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] : X0_iProver_sequential_2 = X0_iProver_sequential_2,
theory(equality) ).
tcf(c_287,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X2_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X2_iProver_shortest_path_2 = X0_iProver_shortest_path_2 )
| ( X2_iProver_shortest_path_2 != X1_iProver_shortest_path_2 )
| ( X0_iProver_shortest_path_2 != X1_iProver_shortest_path_2 ) ),
theory(equality) ).
tcf(c_291,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(X0_iProver_sequential_2) = head_of(X1_iProver_sequential_2) )
| ( X0_iProver_sequential_2 != X1_iProver_sequential_2 ) ),
theory(equality) ).
tcf(c_292,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2] :
( ( tail_of(X0_iProver_sequential_2) = tail_of(X1_iProver_sequential_2) )
| ( X0_iProver_sequential_2 != X1_iProver_sequential_2 ) ),
theory(equality) ).
tcf(c_316,plain,
( ( tail_of(sK10) = tail_of(sK10) )
| ( sK10 != sK10 ) ),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_331,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_369,plain,
( vertex(tail_of(sK10))
| ~ edge(sK10) ),
inference(instantiation,[status(thm)],[c_279]) ).
tcf(c_372,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(X1_iProver_sequential_2,X0_iProver_sequential_2,sK12)
| ~ precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,sK12) ),
inference(instantiation,[status(thm)],[c_246]) ).
tcf(c_374,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2,X2_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(X2_iProver_sequential_2,X0_iProver_sequential_2,sK12)
| ( tail_of(X1_iProver_sequential_2) != tail_of(X2_iProver_sequential_2) )
| ( head_of(X0_iProver_sequential_2) != head_of(X1_iProver_sequential_2) ) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_414,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_237,c_250]) ).
tcf(c_423,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( vertex(X0_iProver_shortest_path_2)
| ~ in_path(X0_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_414,c_266]) ).
tcf(c_427,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( edge(X0_iProver_sequential_2)
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_414,c_269]) ).
tcf(c_428,plain,
( edge(sK10)
| ~ on_path(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_429,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ~ precedes(sK11,sK10,sK12) ),
inference(instantiation,[status(thm)],[c_372]) ).
tcf(c_433,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(X0_iProver_sequential_2) )
| ( tail_of(X0_iProver_sequential_2) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_434,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( tail_of(sK10) != tail_of(sK10) )
| ( head_of(sK11) != head_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_457,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( on_path(sK11,sK12)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_236,c_256]) ).
tcf(c_459,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( on_path(sK10,sK12)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_236,c_257]) ).
tcf(c_481,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(sK11) = head_of(X0_iProver_sequential_2) )
| ( sK11 != X0_iProver_sequential_2 ) ),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_482,plain,
( ( head_of(sK11) = head_of(sK10) )
| ( sK11 != sK10 ) ),
inference(instantiation,[status(thm)],[c_481]) ).
tcf(c_484,plain,
head_of(sK11) = head_of(sK11),
inference(instantiation,[status(thm)],[c_283]) ).
tcf(c_485,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(sK11) = head_of(X0_iProver_sequential_2) )
| ( head_of(sK11) != X0_iProver_shortest_path_2 )
| ( head_of(X0_iProver_sequential_2) != X0_iProver_shortest_path_2 ) ),
inference(instantiation,[status(thm)],[c_287]) ).
tcf(c_488,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( in_path(head_of(X0_iProver_sequential_2),sK12)
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_414,c_268]) ).
tcf(c_491,plain,
on_path(sK11,sK12),
inference(superposition,[status(thm)],[c_414,c_457]) ).
tcf(c_492,plain,
edge(sK11),
inference(superposition,[status(thm)],[c_491,c_427]) ).
tcf(c_493,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_414,c_459]) ).
tcf(c_497,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( vertex(head_of(X0_iProver_sequential_2))
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_488,c_423]) ).
tcf(c_515,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_491,c_497]) ).
tcf(c_636,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_237,c_250]) ).
tcf(c_642,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( on_path(sK10,sK12)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_236,c_257]) ).
tcf(c_643,plain,
on_path(sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_642,c_493]) ).
tcf(c_648,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( vertex(X0_iProver_shortest_path_2)
| ~ in_path(X0_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_636,c_266]) ).
tcf(c_656,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( in_path(tail_of(X0_iProver_sequential_2),sK12)
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_636,c_267]) ).
tcf(c_667,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( vertex(tail_of(X0_iProver_sequential_2))
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_656,c_648]) ).
tcf(c_692,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_643,c_667]) ).
tcf(c_781,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( sequential(sK11,X0_iProver_sequential_2)
| ( sK11 = X0_iProver_sequential_2 )
| ~ edge(sK11)
| ~ edge(X0_iProver_sequential_2)
| ( head_of(sK11) != tail_of(X0_iProver_sequential_2) ) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_782,plain,
( sequential(sK11,sK10)
| ( sK11 = sK10 )
| ~ edge(sK10)
| ~ edge(sK11)
| ( head_of(sK11) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_781]) ).
tcf(c_789,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( tail_of(X0_iProver_sequential_2) = head_of(sK11) )
| ( tail_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = head_of(sK11) )
| ( tail_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = tail_of(X0_iProver_sequential_2) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_2)) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_790,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( tail_of(X0_iProver_sequential_2) = head_of(sK11) )
| ( tail_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = tail_of(X0_iProver_sequential_2) )
| ( head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = tail_of(X0_iProver_sequential_2) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_2)) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_792,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( tail_of(X0_iProver_sequential_2) = head_of(sK11) )
| ( head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = head_of(sK11) )
| ( head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) = tail_of(X0_iProver_sequential_2) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_2)) ),
inference(instantiation,[status(thm)],[c_227]) ).
tcf(c_793,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( edge(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11)))
| ( tail_of(X0_iProver_sequential_2) = head_of(sK11) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_2)) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_794,plain,
( edge(sK0(tail_of(sK10),head_of(sK11)))
| ( tail_of(sK10) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_793]) ).
tcf(c_795,plain,
( ( tail_of(sK10) = head_of(sK11) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_797,plain,
( ( tail_of(sK10) = head_of(sK11) )
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_790]) ).
tcf(c_798,plain,
( ( tail_of(sK10) = head_of(sK11) )
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10) )
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_789]) ).
tcf(c_871,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X1_iProver_shortest_path_2 )
| ( X1_iProver_shortest_path_2 != X0_iProver_shortest_path_2 )
| ( head_of(sK11) != X0_iProver_shortest_path_2 ) ),
inference(instantiation,[status(thm)],[c_287]) ).
tcf(c_872,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(sK11) = head_of(X0_iProver_sequential_2) )
| ( head_of(sK11) != head_of(sK11) )
| ( head_of(X0_iProver_sequential_2) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_485]) ).
tcf(c_1563,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ~ precedes(sK11,sK10,sK12)
| ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_236,c_246]) ).
tcf(c_1565,plain,
~ precedes(sK11,sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_1563,c_105,c_104,c_429]) ).
tcf(c_1575,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_237,c_250]) ).
tcf(c_1734,plain,
! [X0_iProver_sequential_2: iProver_sequential_2,X1_iProver_sequential_2: iProver_sequential_2] :
( precedes(X0_iProver_sequential_2,X1_iProver_sequential_2,sK12)
| ~ on_path(X1_iProver_sequential_2,sK12)
| ~ on_path(X0_iProver_sequential_2,sK12)
| ~ sequential(X0_iProver_sequential_2,X1_iProver_sequential_2) ),
inference(superposition,[status(thm)],[c_1575,c_258]) ).
tcf(c_1795,plain,
( ~ sequential(sK11,sK10)
| ~ on_path(sK10,sK12)
| ~ on_path(sK11,sK12) ),
inference(superposition,[status(thm)],[c_1734,c_1565]) ).
tcf(c_3070,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( X0_iProver_shortest_path_2 != head_of(sK11) )
| ( head_of(sK11) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_871]) ).
tcf(c_3789,plain,
( ~ edge(sK0(tail_of(sK10),head_of(sK11)))
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) != head_of(sK11) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_5295,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(sK11) = head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) )
| ( head_of(sK11) != head_of(sK11) )
| ( head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_872]) ).
tcf(c_5296,plain,
( ( head_of(sK11) = head_of(sK0(tail_of(sK10),head_of(sK11))) )
| ( head_of(sK11) != head_of(sK11) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_5295]) ).
tcf(c_9180,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_237,c_250]) ).
tcf(c_9186,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( vertex(X0_iProver_shortest_path_2)
| ~ in_path(X0_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_9180,c_266]) ).
tcf(c_9191,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( on_path(sK11,sK12)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_236,c_256]) ).
tcf(c_9195,plain,
on_path(sK11,sK12),
inference(global_subsumption_just,[status(thm)],[c_9191,c_491]) ).
tcf(c_9206,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( in_path(head_of(X0_iProver_sequential_2),sK12)
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_9180,c_268]) ).
tcf(c_9215,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( vertex(head_of(X0_iProver_sequential_2))
| ~ on_path(X0_iProver_sequential_2,sK12) ),
inference(superposition,[status(thm)],[c_9206,c_9186]) ).
tcf(c_9230,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_9195,c_9215]) ).
tcf(c_10079,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( tail_of(sK10) = X0_iProver_shortest_path_2 )
| ( tail_of(sK0(tail_of(sK10),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(tail_of(sK10),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(superposition,[status(thm)],[c_692,c_228]) ).
tcf(c_10380,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11) )
| ( head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11) ) ),
inference(superposition,[status(thm)],[c_9230,c_10079]) ).
tcf(c_10448,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) )
| ( tail_of(sK0(tail_of(X0_iProver_sequential_2),head_of(sK11))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_10449,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(sK0(tail_of(sK10),head_of(sK11))) )
| ( tail_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_10448]) ).
tcf(c_11797,plain,
! [X0_iProver_sequential_2: iProver_sequential_2] :
( ( head_of(sK11) = tail_of(X0_iProver_sequential_2) )
| ( head_of(sK11) != head_of(sK11) )
| ( tail_of(X0_iProver_sequential_2) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_3070]) ).
tcf(c_11798,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( tail_of(sK10) != head_of(sK11) )
| ( head_of(sK11) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_11797]) ).
tcf(c_11799,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11798,c_10449,c_10380,c_5296,c_3789,c_1795,c_798,c_797,c_795,c_794,c_782,c_515,c_493,c_492,c_491,c_484,c_482,c_434,c_428,c_369,c_331,c_316,c_104,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRA007+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.46 % Computer : n004.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Wed Sep 23 12:43:21 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.54
% 0.24/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.54
% 0.24/0.54 % Detected problem language: tptp
% 0.24/0.56 % Proving...
% 10.95/4.06 % SZS status Started for theBenchmark.p
% 10.95/4.06 % SZS status Theorem for theBenchmark.p
% 10.95/4.06
% 10.95/4.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.95/4.06
% 10.95/4.06 % ------ iProver source info
% 10.95/4.06
% 10.95/4.06 % git: date: 2026-07-19 20:42:38 +0200
% 10.95/4.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.95/4.06 % git: non_committed_changes: false
% 10.95/4.06
% 10.95/4.06 % ------ Parsing...
% 10.95/4.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.95/4.06
% 10.95/4.06 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 10.95/4.06
% 10.95/4.06 % ------ Preprocessing...%
% 10.95/4.06
% 10.95/4.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.95/4.06 % ------ Proving...
% 10.95/4.06 % ------ Problem Properties
% 10.95/4.06
% 10.95/4.06 %
% 10.95/4.06 % clauses 56
% 10.95/4.06 % conjectures 10
% 10.95/4.06 % EPR 18
% 10.95/4.06 % Horn 38
% 10.95/4.06 % unary 5
% 10.95/4.06 % binary 14
% 10.95/4.06 % lits 176
% 10.95/4.06 % lits eq 46
% 10.95/4.06 % fd_pure 0
% 10.95/4.06 % fd_pseudo 0
% 10.95/4.06 % fd_cond 0
% 10.95/4.06 % fd_pseudo_cond 5
% 10.95/4.06 % AC symbols 0
% 10.95/4.06
% 10.95/4.06 % ------ Input Options Time Limit: Unbounded
% 10.95/4.06
% 10.95/4.06
% 10.95/4.06 % ------
% 10.95/4.06 % Current options:
% 10.95/4.06 % ------
% 10.95/4.06
% 10.95/4.06
% 10.95/4.06 %
% 10.95/4.06
% 10.95/4.06 % ------ Proving...
% 10.95/4.06 %
% 10.95/4.06
% 10.95/4.06 % SZS status Theorem for theBenchmark.p
% 10.95/4.06
% 10.95/4.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.95/4.07
% 10.95/4.07
%------------------------------------------------------------------------------